{
  "id": "2411.09069",
  "version": "v1",
  "published": "2024-11-13T22:50:08.000Z",
  "updated": "2024-11-13T22:50:08.000Z",
  "title": "The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated",
  "authors": [
    "Eduard Schesler",
    "Rachel Skipper",
    "Xiaolei Wu"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "We provide a family of generating sets $S_{\\alpha}$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $\\alpha$ of elements in $V_n$. These generating sets consist of $3$ involutions $\\sigma$, $\\tau$, and $s_{\\alpha}$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-13T22:50:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "20E32"
    ],
    "keywords": [
      "higman-thompson groups",
      "involution",
      "spinal elements",
      "generating sets consist"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}